# How would I complete the square for this equation?

• Sep 1st 2007, 12:19 PM
deathtolife04
How would I complete the square for this equation?
$x^2+y^2-2x+4y=-6$

?
• Sep 1st 2007, 12:23 PM
Jhevon
Quote:

Originally Posted by deathtolife04
$x^2+y^2-2x+4y=-6$

?

piece by piece.

rewrite as: $\left( x^2 - 2x \right) + \left( y^2 + 4y \right) = -6$

and complete the square for what's in the brackets separately (that is, complete the square for the x's and complete the square for the y's), then simplify
• Sep 1st 2007, 12:32 PM
deathtolife04
Quote:

Originally Posted by Jhevon
piece by piece.

rewrite as: $\left( x^2 - 2x \right) + \left( y^2 + 4y \right) = -6$

and complete the square for what's in the brackets separately (that is, complete the square for the x's and complete the square for the y's), then simplify

thanks!

ok so $(x-1)(x-1) + (y+2)(y+2) = -1$

I have been told that my original equation was invalid. But just by looking at $(x-1)(x-1) + (y+2)(y+2) = -1$, couldn't I call that a circle?
• Sep 1st 2007, 12:41 PM
TKHunny
Yes, you have some problems, there. Who told you it was a circle? It's not necessarily invalid, unless it's supposed to be a circle. Where did you get it and what was the original problem statement?
• Sep 1st 2007, 12:45 PM
Jhevon
Quote:

Originally Posted by deathtolife04
thanks!

ok so $(x-1)(x-1) + (y+2)(y+2) = -1$

I have been told that my original equation was invalid. But just by looking at $(x-1)(x-1) + (y+2)(y+2) = -1$, couldn't I call that a circle?

you could have written: $(x - 1)^2 + (y + 2)^2 = -1$

this is not a circle (unless you made an error), since we could not have a negative number on the right hand side if it were a circle.

unless maybe the circle has a radius in the complex plane, but i don't think that makes sense, never did complex analysis
• Sep 1st 2007, 01:04 PM
deathtolife04
Quote:

Originally Posted by Jhevon
you could have written: $(x - 1)^2 + (y + 2)^2 = -1$

this is not a circle (unless you made an error), since we could not have a negative number on the right hand side if it were a circle.

unless maybe the circle has a radius in the complex plane, but i don't think that makes sense, never did complex analysis

ok, i guess i'll just write "imaginary circle" then...
• Sep 1st 2007, 01:05 PM
Jhevon
Quote:

Originally Posted by deathtolife04
ok, i guess i'll just write "imaginary circle" then...

i wouldn't recommend that. are you sure it wasn't a typo. as far as i've seen, the instructions did not ask you to identify the curve, so you don't have to say anything really
• Sep 1st 2007, 01:07 PM
deathtolife04
Quote:

Originally Posted by TKHunny
Yes, you have some problems, there. Who told you it was a circle? It's not necessarily invalid, unless it's supposed to be a circle. Where did you get it and what was the original problem statement?

• Sep 1st 2007, 01:08 PM
deathtolife04
Quote:

Originally Posted by Jhevon
i wouldn't recommend that. are you sure it wasn't a typo. as far as i've seen, the instructions did not ask you to identify the curve, so you don't have to say anything really

well the question just says: classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle

this is the same review that my online home school has been using for years and years, and I have no way of knowing if it's a typo...
• Sep 1st 2007, 01:10 PM
Krizalid
Probably will, 'cause it's really counterproductive a circle with a negative radius :eek:
• Sep 1st 2007, 01:11 PM
Jhevon
Quote:

Originally Posted by deathtolife04
well the question just says: classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle

this is the same review that my online home school has been using for years and years, and I have no way of knowing if it's a typo...

well, it's none of those if it's of the form $(x - h)^2 + (y - k)^2 = c$ where $c < 0$

so maybe "none" is an option. i vaguely remember something about "degenerate conics" but i'm not sure if this applies here. could you say "degenerate circle" i don't know and very much doubt it
• Sep 1st 2007, 01:13 PM
deathtolife04
Quote:

Originally Posted by Jhevon
well, it's none of those if it's of the form $(x - h)^2 + (y - k)^2 = c$ where $c < 0$

so maybe "none" is an option. i vaguely remember something about "degenerate conics" but i'm not sure if this applies here. could you say "degenerate circle" i don't know and very much doubt it

no it doesn't give that as an option. hopefully it's just a typo...

thanks for all your help :D